Maths Section
For description of skills, see Spells Damage Formula I have come up with a theory/model as for the way numerical data is calculated in battle, depending on the different involved parameters: the damage output of one given damaging skills depends on one particular stat of the attacker (ATK or MAG), on elemental sensibility of the target (including physical resistance/vulnerability) and on active buffs/nerfs. '' 'Algorithm' #Choose an attack/skill to use; #Take the actual value of the stat which the skill depends on, for the character who must use it (value indicated on EQUIP screen in the menu, which includes bonuses from weapon and accessories); #Multiply the value by a coefficient, specific to the chosen skill; #Multiply the result by another coefficient, the one describing the elemental sensibility of the target (100% in the Bestiary means a coefficient of 1,...); #Multiply the result by another coefficient, the one describing the buffs/nerfs active on both attacker and target (including Guard status); #Multiply the result by another coefficient, in case of critical hit (2 for critical, 1 otherwise); #Keep the result, which represents the Inferior Bound ; #Multiply the Inferior Bound by a last coefficient, specific to the chosen skill, thus getting the Superior Bound; #The final/actual damage value should be situated between the Inferior Bound and the Superior Bound (both included). Notes: *I recommend to always apply the final coefficient (Step 8) after the others, whereas Steps 3 to 6 may be executed in any order; *The elemental sensibility coefficient (Step 4) can be negative, meaning that the damage will end up negative as well; this is the instance in which the target is healed by the attack that should have damaged them, for a percentage given by the Algorithm; 'Formula' '''STAT' x M''' x '''E x S''' x '''C < D''' < ('''STAT x M''' x '''E x S '''x '''C) x V''' Where: *'''STAT is the actual value of the statistic related to the skill, including assets from equipment; *'M '''is the intrinsic power multiplier related to the skill; *'E is the multiplier of the target's degree of sensibility to the element of the skill. This is stated as a number between -1 and 2 (e.g., 1.25). 1 means the target is neutral to a given element, greater than 1 means it's weak, between 0 and 1 means it's resistant, 0 means immunity, and a negative number means the target absorbs (heals from) an element. *'''S is the multiplier due to the possible buffed/nerfed statuses affecting the attacker and the target. Multiply by 1.8 for a buff and divide by 1.8 for a nerf (if both are buffed, multiply the associated coefficients with one another); (*) *'C' is the critical multiplier: it equals 0 for a Miss, 1 for a normal hit, and 2 for a critical hit; *'V '''is the "variance" multiplier related to the skill. Notes: *A more condensed way to approach to this Formula could be to first calculate the "potential" damage output '''D'o:= STAT x M''' x '''E x S ''' x '''C and consider the final damage D''' being included between it and its variation: 'D'o < '''D < D'''o x '''V ( or D '∈ ['D'o ; '''D'o x '''V] ). *For skills that hit more than once (on one or several targets), the game recalculates the damage for each hit... *(*)Important: There seems to be a glitch regarding the DEF/MDEF DOWN nerfs; in fact, they appear to have no effect at all! Neither on enemies nor on heroes (fixed in Steam release). 'Examples' *''Example 1 :'' I decide to launch a standard physical attack (M'''=1, '''V=1.1) with a character who has an actual 300 of ATK stat (STAT=300), on an enemy whose physical sensibility is 100% (E'=1) ; none of them is buffed/nerfed ('S=1), and the hit is not critical (C'=1). So we have: '''D'o = 300 x 1 x 1 x 1 x 1 = 300 , and 'D'o x '''V = 300 x 1.1 = 330. The final damage my character will deal to the target will then be D''' such as : 300 < '''D < 330. *''Example 2 :'' An enemy with 265 of MAG (STAT=265) casts the skill Water I (M'''=1.4, '''V=1.2) on one of my characters, that I have equipped with a Water Charm (-20% for water) and a Helm (-5% for magic) (which adds up to -25% for water, remains 75%, that is to say E'=0.75) ; still no (de)buff on anyone ('S=1) and no critical hit (C'=1). So we have: '''D'o = 265 x 1.4 x 0.75 x 1 x 1 = 278.25 (to round down to 278) , and 'D'o x '''V = 278.25 x 1.2 = 333.9 (to round up to 334). The final damage my character will take from the enemy's attack will then be D''' such as : 278 < '''D < 334. *Example 3 : I inconsiderately decide to cast Earth I (M'''=1.4, '''V=1.2) on an Earth Golem (E'= -0.25), with a character who has an actual 949 of MAG ('STAT=949) and buffed with Magic Up (S'=1.8) ; the hit happens to be critical ('C=2). So we have: D'o = 949 x 1.4 x (-0.25) x 1.8 x 2 = -1195.74 (to round up to -1196), and '''D'o x '''V =-1195.74 x 1.2 = -1434.888 (to round up to -1435). The final damage my character will deal to the target will then be D''' such as : -1435 < '''D < -1196, Which means that the golem will be healed for 1196 to 1435 HP! 'Nota Bene' This model is just what I could deduce from experimentation; if anyone manages to prove it wrong/inaccurate, feel free to correct it as you like. Coefficient Tables After statistical experimentation (repeatedly recording damage dealt by characters/foes in identical conditions), I have already figured out the intrinsic coefficients '''M' and V''' for a few skills.'' ''(For coefficient '''E, see the Bestiary or Armors)'' (For coefficient '''S', see Statuses)'' 'Offensive Skills' *It is assumed that a skill depending on ATK will result into physical damage, and one depending on MAG into magical damage; except for the Element Attacks which deal damage of a particular element based on the user's ATK stat. *''Guesswork:'' It seems that elemental skills of same level (ex: Fire Attack / Earth Attack... , or Fire I / Water I... , or Earth III / Lightning III... , or Blizzard II / Storm II...) have the same coefficients within a group respectively. *An Eel is equivalent to casting Lightning I; it will react to buffs/nerfs and elemental resistance normally; the only difference is that the caster does not spend MP Healing Skills *Their healing output do not depends on the sensibility or buffs applied to the ally target, but for the rest, they work the same way; you just have to give a value of 1 to the E''' factor, and ignore buffs of the targeted ally. *Only Auto Raise do not depend on buffs of the wearer, as all buffs vanish upon death... (*)'''Important: When all characters have the Spirit Up buff, a glitch will occur that makes the Heal All skill heal 33% less than normal. To factor in this glitch, set S=(2/3) Miscellaneous The attacks are not spells, but will still follow the formula (most likely based on the higher stat of MAG and ATK). 'Enemy Skills' *It is assumed that hero skills also known by enemies will work the same ways that they do for heroes (except for explicit exceptions, then included in the table below) *All poisoning skills seem to work like the Poison skill, whether they deal initial damage or not.(see Special Cases) *As it is not possible to directly know which Stat an enemy skill depends on, it is assumed that a skill dealing physical damage actually depends on ATK, and one dealing elemental damage depends on MAG; although some skills may be really doubtful about this: a few do not have any element of output, and the burst ones are torn between physical and magical... (*): The damage is based on the MAG Stat of the user but deals magic damage of no particular element; this is similar to a Nerf. Damage will react to MAG Down nerf or a character equipped with a Helm/Full Armor. 'Special cases' *These are skills that do not obey the Formula, for various reasons ; however, they still possess their own factor(s), characteristic of their functioning... (*I don't know where on Earth they found this number... but I know it was hell for ME to find it ''--' )'' Burst is affected by the Item+ weapon, and M=1.5 but V is still 2.0. Heals are affected by the Heal+ weapon. 'Nota Bene' (Just like above) These data and assumptions are just what was deduced from experimentation; if anyone manages to find that anything is wrong/inaccurate/missing, feel free to correct it as you like. When testing and trying to get a decimal answer, remember that M can only be rounded down and V can only be rounded up. Damage Damage